New revival phenomena for linear integro–differential equations

  title={New revival phenomena for linear integro–differential equations},
  author={L. Boulton and P. Olver and B. Pelloni and D. Smith},
  journal={arXiv: Analysis of PDEs},
We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in the concrete case of three nonlocal equations that arise in water wave theory and are defined by convolution kernels. Revival in these cases is manifested in the form of dispersively quantised cusped solutions at rational times. We give an analytic description of this phenomenon, and present illustrative numerical simulations. 

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